Gap In MgB2 Research Articles

Theoretical and experimental evidence for a nodal energy gap in MgB2

We present a phenomenological model that strongly suggests that the smaller of the two energy gaps in MgB2, the so-called π gap, contains nodal lines with a six-fold symmetry (i-wave). The model also indicates that the larger gap, the so-called σ gap, is conventional s-wave. The model is an extension of the BCS gap equation that accounts for the elastic anisotropy in MgB2 and the Coulomb repulsion. It is based on a phononic pairing mechanism and assumes no coupling between the two energy gaps in MgB2 at zero temperature. All of the parameters of the model, such as sound velocities and masses, are independently determined material constants. The results agree with a previous ad-hoc hypothesis that the π energy gap has six nodal lines. That hypothesis was motivated by low-temperature measurements of the surface impedance and intermodulation distortion in high-quality thin films. We briefly review experimental evidence in the literature that is relevant to the energy-gap symmetry. We find that the evidence from the literature for s-wave is inconclusive. Our finding is that the π gap has six nodal lines.

Determination of the electron-phonon coupling constants from the experimental temperature dependences of superconducting gaps in MgB2

Experimental temperature dependences Δσ, π(T) of the energy of superconducting gaps for MgB2 samples with the critical temperatures 22 K < T c < 41 K have been fitted by selecting the renormalized electron-phonon coupling constants λ ij with the use of the Moskalenko-Shul system of equations, the expression for the frequency of collective plasma oscillations obtained by Leggett for two-gap superconductors, and two fitting parameters. We previously obtained the dependences Δσ, π(T) by the multiple Andreev reflection spectroscopy of superconductor-constriction-superconductor junctions based on MgB2 with various degree of disorder of the crystal structure. It has been shown that the intraband pairing constants are decisive for the superconductivity mechanism in MgB2; in this case, √V σσ V ππ/V σπ = 8–22 and the ratio of the interband constants α can range from 3 to 11. The set of the Eliashberg coupling constants λ 0 has been qualitatively determined for relatively pure MgB2 with maximum values T c ≈ 40 K. The leading constant is 0.7 < λ σσ 0 ≈ λ eff 0 < 0.9 and depends on the choice of the upper integration limit in the Bardeen-Cooper-Schrieffer (BCS) model and the effective Coulomb repulsion μ iff * . The characteristic ratio for the gap in the σ band is 2Δσ/k B T c = 5.0–6.5.

High-Jc MgB2 Josephson junctions with operating temperature up to 40 K

Sandwich-type MgB2/MgO/MgB2 Josephson junctions with Au or MgB2 interconnection were fabricated using hybrid physical-chemical vapor deposited MgB2 thin films and RF-magnetron-sputtered MgO barrier. The junctions show properties similar to those in high-Jc Nb junctions with Jc up to 275 kA/cm2 at 4 K, which remains nonzero up to 40 K. Critical current modulations by applied magnetic field and constant voltage steps under microwave radiation were observed. Combined with the larger energy gaps in MgB2 than in Nb, the junctions presented here allow simple MgB2 digital circuits to work over 20 K or with a clock speed above 1 THz.

Effect of two-gap structure on flux pinning in MgB2

The magnetic hysteresis loops of MgB2 polycrystalline bulk sample were measured at different temperatures and calculated numerically with different models. The influence of grain orientation, grain boundary pinning, surface pinning and flux creep on the magnetic hysteresis loops of polycrystalline MgB2 was investigated carefully. A two-exponential model taking into account the grain orientation and the flux creep is found to describe the experimental data well, which may be related to the two energy gaps in MgB2.

Anisotropic normal-state properties of theMgB2 superconductor

Based on the experimentally-found existence of two superconducting gaps inMgB2 (one gap associated tothe boron σ-states andthe other to the boron π-states), the different contributions to the transport properties, electrical conductivity andHall coefficient were studied using the full potential-linearized augmented plane wavemethod and the generalized gradient approximation. Four different relaxation times wereneeded to adjust the electrical conductivity and Hall coefficient to experimental values.MgB2 doping was analysed in the rigid band approximation; this permitted adetailed study of the partial substitution of magnesium for aluminium(Mg1−xAlxB2). Other substitutionssuch as AB2 (A = Be, Sc, Zr, Nb and Ta) are also discussed. TheMgB2 σ-bands(boron σ-states), which are associated to the large gap, are very anisotropic atEF, whilethe π bands have very little anisotropic character. InMg1−xAlxB2,Tc diminishes with Al content; the other compounds are not superconductors or have a lowTc. In this work it was found that with electron doping, such as Al substitution, theσ-band conductivity decreases and the corresponding bands become less anisotropic. Theσ-bandcontribution for BeB2 and ScB2 at EF is very small and the anisotropy is much lower. For Zr, Nb and Ta there are noσ-bandsat EF. These results give a clear connection between superconductivity and the character of theσ-band, band conductivity, and band anisotropy. This gives a plausible explanation for the diminution ofTc with differentdoping of MgB2.

The origin of multiple superconducting gaps in MgB2.

Magnesium diboride, MgB2, has the highest transition temperature (T(c) = 39 K) of the known metallic superconductors. Whether the anomalously high T(c) can be described within the conventional BCS (Bardeen-Cooper-Schrieffer) framework has been debated. The key to understanding superconductivity lies with the 'superconducting energy gap' associated with the formation of the superconducting pairs. Recently, the existence of two kinds of superconducting gaps in MgB2 has been suggested by several experiments; this is in contrast to both conventional and high-T(c) superconductors. A clear demonstration of two gaps has not yet been made because the previous experiments lacked the ability to resolve the momentum of the superconducting electrons. Here we report direct experimental evidence for the two-band superconductivity in MgB2, by separately observing the superconducting gaps of the sigma and pi bands (as well as a surface band). The gaps have distinctly different sizes, which unambiguously establishes MgB2 as a two-gap superconductor.

Complicated nature of the gap inMgB2:Magnetic-field-dependent optical studies

We investigated the magnetic field (H)-dependent optical conductivity spectra of MgB2 thin film in the far-infrared region. The H-dependences can be explained by the increase of normal metallic regions embedded in the superconducting background. The area fraction of the normal metallic region increases rather quickly at low field, but slowly at high field. It follows neither H- nor H^{1/2}-dependences. The results suggest the complicated nature of the superconducting gap in MgB2.

Structure of the superconducting gap in MgB2 from point-contact spectroscopy

We have studied the structure of the superconducting gap in MgB2 thin films by means of point-contact spectroscopy using a gold tip. The films were produced by depositing pure boron on a sapphire substrate, using e-beam evaporation, followed by reaction with magnesium vapour. The films have a Tc of 38.6 ± 0.3 K and resistivity of about 20 μΩ cm at 40 K. The point-contact spectra prove directly the existence of a multi-valued order parameter in MgB2, with two distinct values of the gap, Δ1 = 2.3 ± 0.3 meV and Δ2 = 6.2 ± 0.7 meV at 4.2 K. Analysis of the spectra in terms of the Blonder–Tinkham–Klapwijk model reveals that both gaps close simultaneously at the Tc of the film. Possible mechanisms that can explain the intrinsic coexistence of two values of the gap are discussed.